1道数列极限题计算 lim n^2(k/n-1/(

2个回答

lim n^2(k/n-1/(n+1)-1/(n+2)-.-1/(n+k))
=lim n^2{[1/n-1/(n+1)]+[1/n-1/(n+2)].+[1/n-1/(n+k)]
=lim n^2/[n(n+1)]+n^2*2/[n(n+2)]+.+n^2*k/[n(n+k)]
=1+2+.k
=k*(k+1)/2

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